The present invention relates to a method for the determination of a rough trajectory to be followed in a positionally guided manner, executed by a computer, wherein an initial trajectory to be followed in a positionally guided manner is input into the computer, said initial trajectory being described by an initial function so that a corresponding position on the initial trajectory is determined by substituting a scalar trajectory parameter into the initial function.
Such determination methods are generally known. By way of example, reference is made to EP 0 594 699 B1 and to DE 103 55 614.
In EP 0 594 699 B1, the initial trajectory is described as scalar trajectory parameter by means of time. In electronic filters, the trajectory components are determined which correspond to accelerations above and below a limit value, respectively. The above trajectory corresponds to the trajectory components which correspond to accelerations below the limit value. The rough trajectory is used for driving a slow-response drive. The trajectory components with accelerations above the limit value correspond to a fine trajectory. They are used for driving a quick-response drive.
In EP 0 594 699 B1, a special tuning of the possible deflection of the quick-response drive, of the possible acceleration of the slow-response drive and of the maximum permissible trajectory speed ensures that the distance of the rough trajectory from the initial trajectory remains at any time below the maximum possible deflection of the quick-response drive.
In DE 103 55 614 A1, the initial trajectory is also described as scalar trajectory parameter with time. In this document, the initial trajectory is divided into a high-frequency and a low-frequency trajectory component in electronic filters. The low-frequency trajectory component corresponds to the rough trajectory. In DE 103 55 614 A1, it is not guaranteed a priori that the distance of the rough trajectory from the initial trajectory is always below a predetermined threshold independently of the value of the scalar trajectory parameter.
To plan the movement of machines, for example processing machines, particularly machine tools, the following procedure is usually adopted in the prior art: a parts program is input into a computer. The parts program specifies, on the one hand, a contour to be followed in a positionally guided manner and, on the other hand, contains a desired (preferably constant) speed variation, also called trajectory speed in the text which follows. As a rule, the contour already corresponds to an initial trajectory to be followed in a positionally guided manner. If necessary, however, the computer can also determine the initial trajectory in advance by means of the desired contour.
As a rule, the initial trajectory is a two- or three-dimensional trajectory. However, it can also be only one-dimensional, or more than three-dimensional if both the translatory and rotatory movements are to be carried out. It is firstly given as a function of a scalar dimensionless trajectory parameter. Because it is dimensionless, this trajectory parameter is different from time, in particular. However, it is already characteristic of a path traveled along the initial trajectory, at least indirectly.
The dimensionless trajectory parameter is mapped by the computer onto a path traveled along the initial trajectory. Next, the trajectory parameter is mapped onto time by including the desired speed variation. The trajectory now determined is supplied to a test facility. The test facility is a component of the computer. It determines in a clocked manner the nominal position values—possibly also the nominal speed values—for axes to be controlled and outputs these nominal values. Furthermore, it checks the nominal position values and their time derivations (speeds, accelerations, jerks) for the maintenance of predetermined limit values. If at least one of the limit values is exceeded, the trajectory speed must be lowered at least locally and a new run through the test facility must be performed.
In the case of non-redundant kinematics, it to say if exactly one drive or one jointly driven group of drives is to be controlled for each controlled axis, this procedure is completely satisfactory. In the case of redundant kinematics, in contrast, if following the initial trajectory is divided into a rough trajectory for a low-response drive and a fine trajectory for a quick-response drive, wherein the rough trajectory and the fine trajectory complement one another to form the initial trajectory, this procedure only leads to unsatisfactory results. This applies independently of whether the test facility checks only the initial trajectory or the rough trajectory and the fine trajectory for maintenance of the limit values.
If the test facility only checks the initial trajectory for maintenance of the limit values, the limit values could—theoretically—by input in such a manner, naturally, that they can be maintained both by the slow-response drive and by the quick-response drive. Such an input of limit values would be meaningless, however, since any advantage which is to be achieved by the division into rough trajectory and fine trajectory would then be relinquished. If, however, the limit values are input in such a manner that they cannot always be met by both drives, particularly that the acceleration limit value would only be met by the quick-response drive but not by the slow-response drive, there is a risk that the traversing range of the quick-response drive is not maintained, the acceleration limit value of the slow-response drive is not maintained and/or the speed and jerk limit values of at least one of the two drives are not maintained. In addition to the initial trajectory, it must still be checked in both trajectories after the division of the initial trajectory into the rough trajectory and the fine trajectory whether their limit values are maintained. If these limit values are violated,                the trajectory speed must be lowered at least locally,        the scalar trajectory parameter characteristic of the traverse path, different from time, must be remapped under time by including the speed variation which is now changed,        the rough trajectory and the fine trajectory must be redetermined and        it must be checked again whether all limit values are maintained.        
If necessary, this process must even be repeated several times before a reasonably acceptable speed variation can be determined in which the rough trajectory and the fine trajectory are determined in such a manner that all limit values are maintained for both drives. The reason for repeated iterations being required without being able to predict with reliability whether the newly found trajectories maintain the limit values is that a change in the speed variation results in a change in the division of initial trajectory into the rough trajectory and the fine trajectory.
It also may happen with this procedure that the trajectory speed must be lowered locally or globally only because the initial trajectory has been poorly divided into the rough trajectory and the fine trajectory. In other words: if the division of the initial trajectory into the rough trajectory and the fine trajectory had been determined differently, with the speed variation being unchanged, the limit values would have been maintained.
The same problems also occur if the initial trajectory is divided into the rough trajectory and the fine trajectory before the test. This is because, in this case, the test facility can immediately check all nominal position values and their time derivations for maintenance of the limit values but the repeated iteration which may be required and the problem of the possibly only poor division of the initial trajectory into the rough trajectory and the fine trajectory remain.
The abovementioned problems can also be bypassed to only a limited extent by the procedure according to EP 0 594 699 B1. Firstly, this procedure is very computationally intensive, on the one hand, since the variation of acceleration must be determined for the entire initial trajectory and the initial trajectory is divided into the rough trajectory and the fine trajectory by means of the acceleration components. Furthermore, this procedure mandatorily presupposes that the possible traverse path of the quick-response drive, the possible acceleration of the slow-response drive and the maximum trajectory speed are correspondingly matched to one another. If this matching is not guaranteed, the procedure of EP 0 594 699 B1 also exhibits the above problems. Furthermore, if the limit values of the quick-response drive are violated, rough trajectory and fine trajectory must also be redetermined in EP 0 594 699 B1 after the trajectory speed has been lowered, which can lead to other limit values being violated which have been previously maintained.